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Quantum Cloning: Difference between revisions
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==Protocols== | ==Protocols== | ||
*'''Approximate cloning protocols for discrete quantum systems''' Cloning protocols for | *'''Approximate cloning protocols for discrete quantum systems''' Cloning protocols for discrete quantum systems (DV) have been included in this section. The simple case of copying a qubit is an example of these cloning machines. The more general case of these quantum cloning machines is N <math>\rightarrow</math> M cloner which will produce M identical copies of N initial states. The discrete quantum cloning machines can be divided into two main categories: universal and non-universal. | ||
**'''Universal quantum cloning protocols:''' Universal cloning machines produce copies of any arbitrary states. These protocols produce copies which are approximately close to the original state at every round. Also, a universal cloning machine can be | **'''Universal quantum cloning protocols:''' Universal cloning machines produce copies of any arbitrary states. These protocols produce copies which are approximately close to the original state at every round. Also, a universal cloning machine can be | ||
***[[Optimal Universal N-M Cloning|Symmetric or Optimal Cloning]] | ***[[Optimal Universal N-M Cloning|Symmetric or Optimal Cloning]] | ||
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***[[State Dependent N-M Cloning|State-Dependent Cloning]] | ***[[State Dependent N-M Cloning|State-Dependent Cloning]] | ||
***[[Phase Variant Cloning|Phase-Covariant Cloning]]. | ***[[Phase Variant Cloning|Phase-Covariant Cloning]]. | ||
*'''Approximate cloning protocols for | *'''Approximate cloning protocols for continuous variables''' The cloning of several quantum states such as photonic states which are in the regime of continuous variables (CV) have been presented in this section. The N <math>\rightarrow</math> M approximate Gaussian cloning protocol is the most important cloning protocol in CV with a wide variety of application in photonic or quantum oscillator systems. | ||
*'''Probabilistic Cloning''' Another way of having an imperfect cloner is to have a probabilistic cloning machine will produce the copies with some probability of success. In these protocols coping task can succeed with probability, but if it is successful, we can always obtain perfect copies. The probabilistic cloning machines will no longer consists of unitary operations only. But these machines are represented by quantum maps instead. This quantum cloning machine is useful, in particular, in studying the B92 quantum key distribution protocol. | *'''Probabilistic Cloning''' Another way of having an imperfect cloner is to have a probabilistic cloning machine will produce the copies with some probability of success. In these protocols coping task can succeed with probability, but if it is successful, we can always obtain perfect copies. The probabilistic cloning machines will no longer consists of unitary operations only. But these machines are represented by quantum maps instead. This quantum cloning machine is useful, in particular, in studying the B92 quantum key distribution protocol. | ||
**[[Probabilistic Cloning|Probabilistic Cloning]] | **[[Probabilistic Cloning|Probabilistic Cloning]] | ||
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*'''Universal:''' A quantum cloning machine can be universal, meaning that it can copy all the possible input states equally and that the cloning machine is independent of initial states. | *'''Universal:''' A quantum cloning machine can be universal, meaning that it can copy all the possible input states equally and that the cloning machine is independent of initial states. | ||
*'''Optimal:''' A quantum cloning machine can be optimal which means that the average [[fidelity]] of the copies with the original state(s) is maximum over all the possible states and there is no better machine allowed by quantum mechanics for the same setting. | *'''Optimal:''' A quantum cloning machine can be optimal which means that the average [[fidelity]] of the copies with the original state(s) is maximum over all the possible states and there is no better machine allowed by quantum mechanics for the same setting. | ||
*'''Symmetric/Asymmetric:''' A symmetric quantum cloning machine produce the copies which are equally well and close to the original state(s). In other words, the fidelity of all of the copies | *'''Symmetric/Asymmetric:''' A symmetric quantum cloning machine produce the copies which are equally well and close to the original state(s). In other words, the fidelity of all of the copies is the same. In asymmetric cloning machines instead, the fidelity of the output cloned states are different. | ||
==Further Information== | ==Further Information== | ||